2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110134In this article, we derive strong localization results for directed polymers in random environment. We show that at "low temperature" the polymer measure is asymptotically concentrated at a few points of macroscopic mass (we call these points epsilon-atoms). These results are derived assuming weak conditions on the tail decay of the random environment.16 pagesProbability60K37;82B44text